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The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
Constitutive equation; Laws of science; Defining equation (physical chemistry) List of equations in classical mechanics; Table of thermodynamic equations; List of equations in wave theory; List of electromagnetism equations; List of relativistic equations; List of equations in fluid mechanics; List of equations in gravitation; List of photonics ...
In engineering, physics, and chemistry, the study of transport phenomena concerns the exchange of mass, energy, charge, momentum and angular momentum between observed and studied systems. While it draws from fields as diverse as continuum mechanics and thermodynamics , it places a heavy emphasis on the commonalities between the topics covered.
In continuum physics, materials with memory, also referred as materials with hereditary effects are a class of materials whose constitutive equations contains a dependence upon the past history of thermodynamic, kinetic, electromagnetic or other kind of state variables.
The properties are better studied using tensor-valued constitutive equations, which are common in the field of continuum mechanics. For non-Newtonian fluid's viscosity, there are pseudoplastic, plastic, and dilatant flows that are time-independent, and there are thixotropic and rheopectic flows that are time-dependent.
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
The concept of a continuum underlies the mathematical framework for studying large-scale forces and deformations in materials. Although materials are composed of discrete atoms and molecules, separated by empty space or microscopic cracks and crystallographic defects, physical phenomena can often be modeled by considering a substance distributed throughout some region of space.
Analytical or closed-form solutions to the differential equations can be obtained when the geometry, constitutive relations, and boundary conditions are simple enough. Otherwise one must generally resort to numerical approximations such as the finite element method , the finite difference method , and the boundary element method .